Two-dimensional axisymmetric Child-Langmuir scaling law

Journal Article · Thu Oct 15 04:00:00 EDT 2009 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.3243474· OSTI ID:21272730

Ragan-Kelley, Benjamin ^[1]; Verboncoeur, John; Yang, Feng ^[2]

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1. Applied Science and Technology, University of California, Berkeley, California 94720 (United States)
2. Nuclear Engineering, University of California, Berkeley, California 94720 (United States)

The classical one-dimensional (1D) Child-Langmuir law was previously extended to two dimensions by numerical calculation in planar geometries. By considering an axisymmetric cylindrical system with axial emission from a circular cathode of radius r, outer drift tube radius R>r, and gap length L, we further examine the space charge limit in two dimensions. Simulations were done with no applied magnetic field as well as with a large (100 T) longitudinal magnetic field to restrict motion of particles to 1D. The ratio of the observed current density limit J{sub CL2} to the theoretical 1D value J{sub CL1} is found to be a monotonically decreasing function of the ratio of emission radius to gap separation r/L. This result is in agreement with the planar results, where the emission area is proportional to the cathode width W. The drift tube in axisymmetric systems is shown to have a small but measurable effect on the space charge limit. Strong beam edge effects are observed with J(r)/J(0) approaching 3.5. Two-dimensional axisymmetric electrostatic particle-in-cell simulations were used to produce these results.

• OSTI ID: 21272730
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 10 Vol. 16; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
AXIAL SYMMETRY
CATHODES
CURRENT DENSITY
EMISSION
PLASMA SIMULATION
SCALING LAWS
SPACE CHARGE
TWO-DIMENSIONAL CALCULATIONS